Green face on the main view means the city is unhealthy. Red face on the main view means it's unhappy.
In Civ 4 you have to worry about two factors. Whether the population exceeds it's capacity to keep people happy (which temples and luxuries and such help with) and whether or not your population exceeds it's capacity to keep people healthy.
For health, special food resources (wheat, rice, corn, clams, fish, etc), forests, fresh water, and a few buildings help. Population, flood plains and (I think) jungles hurt and a few buildings (forge, factory, coal plants) hurt.